Question $1(20$ points$)$: In this question you will demonstrate that you understand how the data stored in caches is organized. Assume that each cache operates in a machine with a $32-$bit virtual address.

$(10$ points$)$ For each of the cache configurations below, indicate how many bits are used for byte offset, for cache index, and for tag.

$\backslash$table$[[$Cache capacity,Associativity,Size of Cache Block,Tag Size,Index Size,Byte offset size$],[64$KB$,$Direct mapped,$128$ bytes,,,$],[32$KB$,2-$way,$64$ bytes,,,$],[32$MB$,8-$way,$512$ bytes,,,$]]$

$10$ points The table below contains the same cache organizations listed in the table above. Using binary notation, provide the value of the tag and the value of the cache index for a memory reference to the address $0$xABCD EF$78.$ Also indicate which word within the block is being accessed. The word at offset $0$ is word #$0,$ the word at offset $4$ is word #$1,$ etc.

$\backslash$table$[[\backslash$table$[[$Cache$],[$capacity$]],$Associativity,Cache Block,Tag,Index,word accessed$],[64$KB$,$Dir. map.,$128$ bytes,,,$],[32$KB$,2-$way,$64$ bytes,,,$],[32$MB$,8-$way,$512$ bytes,,,$]]$